Calculating Flow Rate with Pressure and Diameter

Calculate GPM and LPM from Pressure and Pipe Diameter

Standard inner dimension of the pipe/nozzle.

Pressure measured at the point of discharge.

0.98 – Smooth Pipe / Nozzle 0.80 – Average Pipe Outlet 0.62 – Sharp-edged Orifice 0.50 – Short Tube The ratio of actual flow to theoretical flow.

Calculated Flow Results:

US Gallons Per Minute 0.00 GPM

Liters Per Minute 0.00 L/min

function calculatePipeFlow() { var d = parseFloat(document.getElementById('pipeDiameter').value); var p = parseFloat(document.getElementById('fluidPressure').value); var c = parseFloat(document.getElementById('dischargeCoeff').value); var resultDiv = document.getElementById('flowResult'); if (isNaN(d) || isNaN(p) || isNaN(c) || d <= 0 || p < 0) { alert("Please enter valid positive values for diameter and pressure."); return; } // Using the Bernoulli derivative formula for GPM: // Q = 29.84 * C * d^2 * sqrt(P) // Where Q is GPM, C is discharge coefficient, d is diameter in inches, P is PSI var gpm = 29.84 * c * Math.pow(d, 2) * Math.sqrt(p); var lpm = gpm * 3.78541; // Calculate velocity for context (v = Q/A) // Area in sq ft = (pi * (d/24)^2) // Q in cubic feet per second = GPM / 448.83 var areaSqIn = Math.PI * Math.pow((d / 2), 2); var velocityFPS = (gpm * 0.3208) / areaSqIn; document.getElementById('resGPM').innerText = gpm.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('resLPM').innerText = lpm.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('resVelocity').innerHTML = "Estimated Fluid Velocity: " + velocityFPS.toFixed(2) + " ft/s"; resultDiv.style.display = 'block'; }

How to Calculate Flow Rate from Pressure and Diameter

In hydraulics and fluid mechanics, determining the flow rate (the volume of fluid passing through a point per unit of time) is critical for designing irrigation systems, fire protection networks, and industrial piping. When you know the internal diameter of a pipe or nozzle and the pressure of the fluid, you can calculate the discharge using the principles of Bernoulli's Equation.

The Flow Rate Formula

The standard simplified formula for calculating flow rate in Gallons Per Minute (GPM) when working with water is:

Q = 29.84 × C_d × d² × √P

• Q: Flow rate in Gallons Per Minute (GPM).
• C_d: Discharge Coefficient (accounts for friction and turbulence).
• d: Internal diameter of the opening in inches.
• P: Fluid pressure at the opening in Pounds per Square Inch (PSI).

Understanding the Discharge Coefficient (C_d)

Not all openings are created equal. The shape of the exit point affects how efficiently water leaves the pipe. This efficiency is represented by the Discharge Coefficient:

Type of Opening	Typical Cd Value
Smooth, Well-Rounded Nozzle	0.97 – 0.99
Short, Flush Pipe Outlet	0.80 – 0.82
Sharp-Edged Orifice	0.61 – 0.63

Real-World Example Calculation

Suppose you have a 2-inch diameter pipe discharging water into the atmosphere, and your pressure gauge reads 50 PSI. If we assume a standard sharp-edged orifice (C_d = 0.62):

1. Square the diameter: 2 × 2 = 4.
2. Find the square root of the pressure: √50 ≈ 7.07.
3. Multiply by the coefficient and the constant: 29.84 × 0.62 × 4 × 7.07.
4. Result: Approximately 523.21 GPM.

Frequently Asked Questions

Does pipe length affect flow rate?

Yes. This calculator assumes the pressure is measured at the point of discharge. If you measure pressure at the pump and have 100 feet of pipe, friction loss will decrease the actual pressure and flow rate at the end of the line.

What happens if I double the diameter?

Because diameter is squared in the formula, doubling the diameter actually quadruples the potential flow rate (assuming pressure remains constant).

Is this accurate for thick fluids like oil?

This specific formula is calibrated for water. For high-viscosity fluids like oil or heavy syrups, additional factors for Reynolds number and viscosity must be applied.